$B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 2x + 6$ and $ BC = 7x + 1$ Find $AC$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {2x + 6} = {7x + 1}$ Solve for $x$ $ -5x = -5$ $ x = 1$ Substitute $1$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 2({1}) + 6$ $ BC = 7({1}) + 1$ $ AB = 2 + 6$ $ BC = 7 + 1$ $ AB = 8$ $ BC = 8$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {8} + {8}$ $ AC = 16$